That's the problem, probability just doesn't work in markets for most, normal trading styles. You have three counterexamples that intend to demonstrate the need or at least benefit of having knowledge in probability.
1.) you wish to be around to trade after a series of drawdowns ( a mathematical concept).
rebuttal: A mathematical concept can be used without knowledge of the mathematical concept being used. Ever heard of the 2% rule? Even though it is extremely naive mathematically, it should do fine for most. And any perfect probability system for how much to trade requires a perfect probability model of the market you are trading (which is impossible), so even if you had a complex grasp of probability, you may not even be able to do better than the ad hoc 2% rule.
2.)Perhaps you would play BlackJack at a the casino without math (hardly likely)
rebuttal: This is a faulty analogy. In a gambling game, the random process known as the card game is perfectly modeled. The market can never be perfectly modeled in the same fashion, rendering probabilistic methods ineffective for most trading styles.
3.)or go to the racetrack without a sense of your odds or your edge (hardly likely).
rebuttal: This point of yours is misleading, because the sentence in general is true. You definitely would not go blindly bet on horses without any good reason (i.e. without your odds or edge). However, there is an added implied yet false idea: that having a sense of your odds or edge demands a knowledge of probability.
The mind is a vastly complex pattern recognition system. Recent research has even shown young children learn like a computer using Bayesian techniques. It's the reason why most funds are not quant funds, the reason why it takes so long for an algorithm to replicate the results of humans in games of logic, etc. Don't try to buy the cart before the horse with this one
. Note, I am not saying an algorithm cannot outperform a human -- that would be as naive as saying it also cannot beat a human in chess. All I am saying is most people can perform their best without directly understanding probability. To extend the chess metaphor, you can phrase the question of the best move as which one has the highest probability of winning the game. Obviously, humans skip over the pedantic weight and simply think up their best solution. And over years of doing this (and studying the works of humans who had done this), the current set of humans (and many past sets) are (were) really good at chess.
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